Ion sources used in mass spectrometry produce continuous or quasi-continuous beams of charged particles. Even in the case of pulsed operation of an ion source, accumulation of charged particles during several cycles of operation in a special storage device may be necessary. Therefore, in the case of pulsed operation of mass-analysers, special devices are used to ensure decomposition or breaking-up of a continuous beam of charged particles or the contents of a storage device, into separate portions and transportation thereof to the mass-analyser input. In recent devices used for transportation of charged particles, the tasks of cooling and spatial compression of charged particle packets for the purpose of a reduction of their emittance (the size of a packet of particles in phase-space coordinates) can also be solved efficiently, and additional manipulations can be performed with the charged particles during transportation (for example, fragmentation of charged particles, generation of secondary charged particles, selective extraction of charged particles to be subject to detailed analysis, etc.).
Several types of radio-frequency (RF) devices are used in mass spectrometry for charged particle manipulation. The first group of such devices includes mass analysers (as well as mass separators and mass filters). The purpose of such devices is the selection of those particles featuring particular mass-to-charge ratio, from the totality of charged particles. The main types of RF mass analysers include quadrupole mass filters and ion traps.
Radio-frequency quadrupole mass filters and ion traps proposed by Paul are known starting from about 1960s. Both types of mass analysers have been proposed in U.S. Pat. No. 2,939,952. Rather recently, linear ion traps were proposed, with radial ejection of charged particles from the trap (U.S. Pat. No. 5,420,425) and ejection of ions from the trap along the axis (U.S. Pat. No. 617,768). A detailed description of the principle of operation of said devices can be found, for example, in R. E. March, J. F. J. Todd, Quadrupole Ion Trap Mass Spectrometry, 2nd edition, Wiley-Interscience, 2005; F. J. Major, V. N. Gheorghe, G. Werth, Charged Particle Traps, Springer, 2005; G. Werth, V. N. Gheorghe, F. J. Major, Charged Particle Traps II, Springer, 2009.
Functioning of quadrupole mass filters is based on the theory of solution stability of the Mathieu equation (see, for example, N. W. McLachlan, Theory and Application of Mathieu Functions, Claredon Press, Oxford, 1947 (chapter 4) or M. Abramovitz and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, 10ed., NBS, 1972 (chapter 20)). In the case of well-selected parameters of the intensity of quadrupole DC electric field, intensity of quadrupole RF field and the frequency of quadrupole RF field, charged particles having a particular mass-to-charge ratio would pass through the RF quadrupole mass filter. The other charged particles would lose the stability of their trajectories, and would be lost outside the boundaries of the channel of the mass filter.
Operation of mass analysers of the ion trap type is generally based on the theory of the Mathieu equation. In these mass analysers, a quadratic or nearly quadratic electric field is used, obtained through application of ideal hyperbolic electrodes, and the analysers are filled with a light gas at low enough pressure. In such devices, after slowing down the speed of motion of the charged particles due to multiple collisions with the molecules of neutral gas, the particles would then sequentially be extracted from the device by means of swinging/oscillating of the group of charged particles having the required mass-to-charge ratio, with the help of an RF electric field having the required frequency. The picture described above is somewhat approximate, since the practical ion trap mass spectrometry has developed and employed rather sophisticated methods for isolation, fragmentation and selective ejection of charged particles from ion traps by means of the action of specially configured RF fields on the particles.
Another important group of RF devices includes RF transporting devices for ion beams. The purpose of such devices is the confining of a beam of charged particles having different masses, within a bounded region inside the device (for example, near the axis of the device), and transfer of charged particles from one point within the space (point of inlet) to another point within the space (point of outlet).
A wide class of such devices is based on application of a two-dimensional multipole field, or approximate multipole field, extended along the third coordinate. The devices are used, for example, for transfer of ions from gas-filled ion sources operating at rather high gas pressures, into devices for mass-analysis of ions, operating at considerably lower pressure of gas, or in vacuum. Because of the fact that said linear multipole ion traps are not used directly for mass analysis, the requirements towards a strictly quadratic or strictly multipole field would not be vital, and for the purpose of simplification of the production technology while manufacturing such devices, hyperbolic and multipole electrodes, as a rule, would be replaced with cylindrical rods or even more coarsely shaped electrodes.
When charged particles are transferred into a linear multipole trap, collisions of the charged particles with gas molecules reduce their kinetic energy and force the particles to be groped near the axis of the device (U.S. Pat. No. 4,963,736). This ensures such an important function like beam cooling and spatial compressing of the beam of charged particle for the purpose of reduction of the beam emittance (i.e., the volume of an ensemble of charged particles, corresponding to the beam, in phase space). An RF electric field is capable of confining charged particles in a radial direction, at a stage where the reduction of kinetic energy of charged particles has not yet taken place, even in the case of relatively high kinetic energies, and “compresses” the particles towards the axis in the course of the loss of their kinetic energy.
The gas-filled linear multipole ion beam transporting devices described above are frequently used simultaneously, as collision cells for fragmentation of charged particles in tandem mass spectrometers (for example, see U.S. Pat. No. 6,093,929). A DC electric field directed along the axis of the device, the field created by additional electrodes, can be used for forced transfer of charged particles along the channel of transfer (ion transporting device proposed in U.S. Pat. No. 5,847,386, collision cell for fragmentation of ions proposed in U.S. Pat. No. 6,111,250).
If the ends of a linear multipole ion transporting device are closed using barriers formed by an electric field, another type of RF device used in mass spectrometry is formed—a linear multipole ion trap, or a storage device for charged particles. Such traps are widely used to accumulate charged particles and pulse transmission of charged particles into an analysing device (U.S. Pat. No. 5,179,278, WO02078046, U.S. Pat. Nos. 5,763,878, 6,020,586, 6,507,019 and GB2388248). Multipole ion traps are also frequently used to initiate task-oriented ion-molecular reactions between charged particles and neutral particles (U.S. Pat. Nos. 6,140,638 and 6,011,259), or electrons (patent Nos. GB2372877, GB2403845 and GB2403590), or charged particles with opposite charges (U.S. Pat. No. 6,627,875), to provide additional fragmentation of charged particles due to exposure of the same to an impact, for example, of photons, or other external physical factors.
The RF ion trap proposed by Paul, or a linear trap, can also be used for the same purpose as a multipole linear trap, when the total amount of ions is injected at once from the trap into an analysing device due to a pulse of electric voltage, instead of consecutive resonance ejection of the desired groups of ions (patent Nos. WO2006/129068 and US2008/0035841). In a similar way, a multipole linear trap, wherein the injection into the analysing device is made mass-selective, can be used as a rough mass filter, which selects the required groups of charged particles for further detailed analysis (patent No. US2007/0158545).
There are devices known to have functions similar to the above-mentioned transporting devices, which include transporting devices and/or storage devices wherein electrodes are used, in the form of an array of plates with apertures, and to which electrodes RF voltages are applied, with phase shift between adjacent plates (U.S. Pat. Nos. 6,812,453, 6,894,286 and 5,818,055), or between the parts forming one plate (patent No. PCT/GB2010/001076). In that case, because of the symmetry of electrodes, the generated RF field near the axis of the device would be practically zero, whereas it would grow abruptly near the boundaries of the transporting channel. Therefore, like in the case of the linear multipole ion transporting devices, the charged particles would be repelled from the electrodes and confined by the RF field within a limited space surrounding the axis of the device, and in the course of reduction of their kinetic energy due to collisions with gas molecules, the charged particles would be grouped near the axis of the device.
One can see that in the case of an absence of additional electric fields in the vicinity of the axis of the device, the forces enabling the movement of charged particles along the axis of the transporting device would practically be absent due to symmetry of the electrodes and high frequency of the electric field (U.S. Pat. Nos. 5,818,055 and 6,894,286), and the transfer of charged particles along the length of the channel for transportation would not be very efficient. Indeed, the capture of charged particles moving along the axis of the device is not mentioned in U.S. Pat. Nos. 5,818,055 and 6,894,286; furthermore, the particles having different masses and different initial conditions (coordinates and velocities) move along the channel of transportation with different effective velocities, and as a result, there would be no separation of the beam of charged particles into individual spatially separated and synchronically transferred packets of charged particles.
The superposition of radially non-uniform RF electric field, which enables localisation of charged particles in the vicinity of the axis of the device along the radial direction, and quasi-static progressive wave of electric field along the axis of the device enabling splitting of the beam of charged particles having different masses into spatially separated packets and synchronous transportation of said packets along the axis of the device may be the most successful solution from among the above-mentioned solutions (U.S. Pat. No. 6,812,453 and PC T/GB2010/001076).
However, since the positively charged particles are grouped in the vicinities of minima of the progressive wave of potential of the quasi-static electric field, and negatively charged particles are grouped in the vicinities of maxima of the progressive wave of potential of the quasi-static electric field, it would not be possible to ensure transportation of positively and negatively charged particles in an integrated packet of charged particles using this method.
The functioning of the majority of RF mass-spectrometry devices is based on the property of an RF electric field to “eject” the charged particles, regardless of the polarity of their charge, from the area of high amplitude of electric field into the area with lower amplitude of electric field. This property has been the consequence of the inertia of motion of charged particles having non-zero masses, under the influence of a fast oscillating electric field.
This phenomena is described quantitatively with the help of the theory of effective potential or pseudopotential, first introduced by P. L. Kapitza (see L. D. Landau, E. M. Lifshitz, Mechanics, Ser. Theoretical Physics, M., Fizmatlit, 2004, p. 124-127; G. M. Zaslav sky and R. Z. Sagdeev, Introduction to nonlinear physics: from pendulum to turbulence and chaos, M., Nauka, 1988, p. 49-51 and p. 52-54; M. I. Yavor, Optics of Charged Particle Analysers, Ser. Advances of Imaging and Electron Physics, Vol. 157, Elsevier, 2009, p. 142-144). That is, suppose the frequency ω of oscillations of electric field {right arrow over (E)}(x, y, z, t), which follows the law {right arrow over (E)}(x, y, z, t)={right arrow over (E)}0(x, y, z)cos(ωt+φ), is high enough (where {right arrow over (E)}0(x, y, z) is the amplitude of oscillations of electric field in a point within the space (x, y, z), ω—frequency of oscillations, φ—initial phase of oscillations, t—time), and the displacement of charged particle having the mass m and charge q, during one period of oscillations of the electric field is small, then the motion of the charged particle can be represented as an “averaged” or “slow” motion, with an added rapid oscillating motion, featuring, however, small amplitude. In that case, the equation for averaged motion would look like as if the averaged motion takes place within electric field having the potential Ū(x, y, z)=q|{right arrow over (E)}0(x, y, z)|2/(4mω2), where the values q, {right arrow over (E)}0(x, y, z), m and ω characterizing the oscillating electric field and the charged particle, have been defined above. The details and substantiation of the theory can be found in the references cited above.
Due to the fact that the expression for potential Ū(x, y, z) includes charge q and mass m, the potential Ū(x, y, z) affects equally both positively and negatively charged particles, and the effect is also dependent on the mass of a charged particle. In case of a real electric potential U(x, y, z) positively charged particles would undergo a force directed reversely with respect to the gradient of electrical potential, and negatively charged particles would undergo a force directed along the gradient of electrical potential, whereas such force would not be dependent on the mass of a particle. From the expression for potential Ū(x, y, z) it follows, that a charged particle would be «pushed out» from the area where the amplitude of oscillations of the RF field is high, into the area where said amplitude of oscillations of the RF field is lower (that is, from the area where the potential Ū(x, y, z) has a higher value, the particle would move into the area where the potential Ū(x, y, z) has a lower value). The extracting action of the RF electric field is not dependent on the polarity of charged particle, and moves both positive and negative charged particles in the same direction. The extracting action of the RF electric field is weaker with respect to those charged particles having heavier masses, than with respect to lighter charged particles. The extracting action of the RF electric field can be controlled by varying the frequency of oscillations of the electric field.
The potential Ū(x, y, z) is called an effective potential, or a pseudopotential, and represents a useful mathematical tool for describing and analysing the averaged motion of a charged particle (though in fact, it does not actually correspond to any physical fields). We shall take for granted, some of its properties. For electric field {right arrow over (E)}(x, y, z, t), which varies with time t under the law of harmonic oscillations {right arrow over (E)}(x, y, z, t)={right arrow over (E)}0(x, y, z)cos(ωt+φ) with a constant amplitude {right arrow over (E)}0(x, y, z) at a point (x, y, z), with a constant frequency a and with a constant phase shift φ=const, the pseudopotential Ū(x, y, z), which affects a charged particle having the charge q and mass m, is calculated using the above formula Ū(x, y, z)=q|{right arrow over (E)}0(x, y, z)|2/(4mω2). If the phase of the RF field is not constant over the entire space, but varies from point to point in a predetermined manner φ=φ(x, y, z), so that the law of variation of the (RF electrical field with time t has a more sophisticated form {right arrow over (E)}(x, y, z, t)={right arrow over (E)}0(x, y, z)·cos(ωt+φ(x, y, z))={right arrow over (E)}c(x, y, z)·cos ωt+{right arrow over (E)}s(x, y, z)·sin ωt, where {right arrow over (E)}c(x, y, z) is the amplitude of harmonic component cos wt in the point of space (x, y, z), {right arrow over (E)}s(x, y, z) is the amplitude of harmonic component sin at in the point of space (x, y, z), and the values {right arrow over (E)}0(x, y, z), ω and φ(x, y, z) were defined earlier, then the pseudopotential Ū(x, y, z) corresponding to the given RF electrical field would be calculated using the formula Ū(x, y, z)=q(|{right arrow over (E)}c|2+|{right arrow over (E)}s|2)/(4mω2), where q is the charge of a particle, and m is its mass. If the RF field under consideration is a time-dependent periodic function, so that the electric filed intensity {right arrow over (E)}(x, y, z, t) in the point of space (x, y, z) at the point of time t can be represented as a Fourier series in the form of {right arrow over (E)}(x, y, z, t)=Σ{right arrow over (E)}c(k)(x, y, z)cos(kωt)+{right arrow over (E)}s(k)(x, y, z)sin(kωt), where {right arrow over (E)}c(k)(x, y, z) is the amplitude of harmonic component cos kωt of electric field in the point of space (x, y, z), {right arrow over (E)}s(k)(x, y, z) is the amplitude of harmonic component sin kωt of electric field in the point of space (x, y, z), k is the number of harmonic component, ω is fundamental frequency of the RF electric field, then the pseudopotential Ū(x, y, z) of such RF electric field would be calculated as a sum of contributions of individual harmonic components, using the formula Ū(x, y, z)=qΣ(|{right arrow over (E)}c(k)(x, y, z)|2+{right arrow over (E)}s(k)(x, y, z)|2)/(4mω2k2), where q is the charge of a particle, and m is its mass. If in addition to the RF electric field {right arrow over (E)}(x, y, z, t), there is an electrostatic field having potential of U(x, y, z), the electrostatic potential U(x, y, z) and the pseudopotential Ū(x, y, z) would be summed. If there are several different RF electric fields with essentially different frequencies, then individual pseudopotentials would be summed for these electric fields, however, if the difference between the frequencies of these RF fields is insignificant, this rule would not be valid. If, for the purpose of simulation of charged particle kinetic energy reduction as a result of collisions with gas molecules, an effective viscous friction is introduced, having an impact on the charged particle with a force {right arrow over (F)}=−γ({right arrow over (ν)}−{right arrow over (ν)}0), where {right arrow over (ν)}(t) is the velocity of particle at time t, {right arrow over (ν)}0(x, y, z) is the velocity of gas molecules in the point (x, y, z), and γ is the viscous friction coefficient, which does not depend on time, coordinates, and electric field, then the result of “slow” motion of charged particle would be as if all the three factors (electrostatic potential, pseudopotential and viscous friction) were affecting the charged particle simultaneously and independently.
It should be emphasised that the description of motion of a charged particle, using pseudopotential, only represents a mathematical approximation, obtained under certain assumptions as regards the motion of charged particle, and may not correspond to its actual motion. In this respect, for the purpose of analysis of charged particle motion in the above mentioned radio-frequency quadrupole mass filters and radio-frequency ion traps, it would be necessary to perform a rigorous analysis of motion of a charged particle in the actual electric fields (i.e., Mathieu equation theory), in order to obtain the correct structure of the zones of stability of motion. The approach based on the use of pseudopotential would not give a correct solution, because under the conditions where a charged particle moves near the boundary of the zone of stability, and a resonance takes place between “slow” oscillations of the charged particle and the RF electric field, the displacement of the charged particle during one period of the RF electric field under no conditions could be considered to be small.
The present inventors have considered the operation of the device of U.S. Pat. No. 6,812,453 in more detail.
The device under consideration contains a system of electrodes representing a series of coaxially positioned plates with apertures arranged to create internal space between the electrodes, the space directed along the longitudinal axis of the device, and intended for transmission of ions within the same. The device also includes a source of power supply, which provides supply voltage to be applied to the electrodes, including alternating high frequency voltage component, the positive and negative phases of which are applied alternately to the electrodes, and quasi-static voltage component, for creation of which, static or quasi-static voltages are applied to the electrodes successively and alternately, in particular, in the form of unipolar or bipolar pulses of a DC voltage.
The said device creates an electric field, the intensity of which {right arrow over (E)}(x, y, z, t) is described by the expression {right arrow over (E)}(x, y, z, t)={right arrow over (E)}a(x, y, z, t)+{right arrow over (E)}0(x, y, z)ƒ(t), where {right arrow over (E)}a(x, y, z, t) is a quasi-static electric field varying along the length of the channel for charged particles transportation, depending on the spatial coordinates (x, y, z) and time t, {right arrow over (E)}0(x, y, z) is time-independent and non-uniform, at least in a radial direction, amplitude of the RF electric field, depending on spatial coordinates (x, y, z) and independent on time t, ƒ(t)=cos(ωt+φ) is the rapidly oscillating function of time t, which in this particular case describes strictly harmonic oscillations with the frequency ω and initial phase φ. Quasi-static behaviour of the function {right arrow over (E)}a(x, y, z, t) and the rapidness of oscillations of the function ƒ(t) are understood in the sense that during a period where the function ƒ(t) has time to perform several oscillations, the function {right arrow over (E)}a(x, y, z, t) remains practically unchanged. Mathematical notation of this condition is written in the form of inequality |∂{right arrow over (E)}a/∂t|2/|{right arrow over (E)}0|2<<|df/dt|2, which should be satisfied, in order that the device would function properly. Thereby variation of the electric field {right arrow over (E)}(x, y, z, t) with time would have two time scales: a “fast time”, during which the value of the function {right arrow over (E)}0(x, y, z)ƒ(t) would be noticeably changed, and a “slow time”, during which the value of the function {right arrow over (E)}a(x, y, z, t) would be noticeably changed.
FIGS. 1 to 9 assist with understanding the operation of the device of U.S. Pat. No. 6,812,453. FIG. 1 demonstrates a round diaphragm used as a single electrode for the device according to U.S. Pat. No. 6,812,453. FIG. 2 shows the arrangement of the aggregate of round diaphragms with respect to the channel for charged particles transfer, according to U.S. Pat. No. 6,812,453. FIG. 3 shows the distribution of axial component of the intensity of electric field according to U.S. Pat. No. 6,812,453 along the length of the channel for charged particle transportation, for a series of close points in time t, t+δt, t+2δt, t+3δt, . . . (that is, in a “fast” time scale). FIG. 4 shows variation of the envelope of axial component of the electric field of U.S. Pat. No. 6,812,453 along the length of channel, for a number of points in time t and t+Δt, located sufficiently far from each other (that is, in a “slow” time scale). The radial component of the electric field equals zero at the axis of the device of U.S. Pat. No. 6,812,453 due to the symmetrical configuration of the electrodes. FIG. 5 shows a two-dimensional distribution of pseudopotential Ū0(x, y, z) along the length of the channel for charged particle transportation, and in a radial direction of the channel for transportation, which corresponds to the RF electric field according to U.S. Pat. No. 6,812,453. FIG. 6 shows possible two-dimensional distribution (at some point in time) of the potential Ua(x, y, z, t) of the quasi-static electric field {right arrow over (E)}a(x, y, z, t) of U.S. Pat. No. 6,812,453. FIG. 7 shows possible distribution of the potential Ua(x, y, z, t) of quasi-static electric field {right arrow over (E)}a(x, y, z, t) of U.S. Pat. No. 6,812,453, along the length of the channel for charged particle transportation. FIG. 8 shows possible summary electric voltages, which can be applied to the first, second, third, fourth electrode, respectively, in each group of four repetitive electrodes, according to U.S. Pat. No. 6,812,453. (In these examples, the simplest possible case is considered, of the progressive wave of quasi-static potential Ua(x, y, z, t), formed along the channel intended for the motion of charged particles, according to U.S. Pat. No. 6,812,453, viz., the case of a wave having purely sinusoidal waveform.)
According to U.S. Pat. No. 6,812,453 the charged particles are “forced” towards the axis of the device as a result of the action of the RF field and formation of the pseudopotential Ū0(x, y, z) over the radius thereby forming a barrier farther from the axis of the device, and after damping of kinetic energy to equilibrium value, appear to be collected in the neighbourhood of the axis of the device. Due to the presence of the distribution of the quasi-static electric potential with alternating local minima and maxima along the axis of the device, positively charged particles are not just concentrated around the axis of the device, but are collected in local minima of the quasi-static electric potential, as soon as their kinetic energy proves to be lower than the local maxima of the quasi-static electric potential. Respectively, the negatively charged particles, after cooling as a result of collisions with gas molecules, are collected in local maxima of the quasi-static electric potential (the positively charged particles are affected by the force directed against the gradient of the electric potential, while negatively charged particles are affected by the force directed along the gradient of the electric potential).
The fact that at some interval along the length of the axis (in particular, in the neighbourhood of the minima of electric potential for positively charged particles and in the neighbourhood of the maxima of electric potential for negatively charged particles), while moving away from the axis, the radial electric field of quasi-static potential repels the charged particles from the axis of the device, is of no importance, since the repelling action of the RF field, returning the charged particles back to the axis of the device is overbalancing i.e. dominant. When the wave of the quasi-static potential Ua(x, y, z, t) travels slowly along the axis of the device, it captures the charged particles, located near the axis of the device in the neighbourhood of local maxima and minima of the quasi-static potential, while forcing the particles having different masses and different kinetic energies to move synchronously. The process is shown schematically in FIG. 9. Note that this results in alternating groups of positively and negatively charged particles.
Numerical simulation by the present inventors of the actual motion of charged particles in the described electric fields confirms this qualitative picture of motion. For output devices operating in pulsed mode, this method of separation of a continuous flow of charged particles into discrete portions seems to be the most successful. With a correct setting of time intervals between arrivals of individual discrete portions of charged particles from the output of the transporting device and correspondingly, to the input of the next device (which, as a rule, represents a mass analyser operating in pulsed mode), and the time of the next analysis of arrived portion of charged particles, this method allows analysis of all the charged particles from the continuous beam into the analyser, practically without losses.
However, the device of U.S. Pat. No. 6,812,453 does not provide a capability of combining positively and negatively charged particles in a single transported packet.